Hi there,
Yes - all these routes are covered by the Japan Rail Pass. 7 day rail pass is ¥28,300, a 14 day rail pass is ¥45,100 and a 21 day rail pass is ¥57,700. To check whether a rail pass is cheaper we need to calculate the real ticket costs of this route and compare:
- Tokyo > Odawara: ¥3640, (35mins, 83km)
- Odawara > Kyoto: ¥11750, (160mins, 429km)
- Kyoto > Nara: ¥690, (44mins, 41km)
- Nara > Kyoto: ¥690, (48mins, 41km)
- Kyoto > Osaka: ¥1680, (27mins, 42km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Himeji: ¥5130, (68mins, 130km)
- Himeji > Hiroshima: ¥8070, (60mins, 249km)
- Hiroshima > Kyoto: ¥10790, (126mins, 380km)
- Kyoto > Nagoya: ¥5440, (49mins, 147km)
TOTAL: ¥48420 for 10 legs
As you can see, both 7 and 14 day rail passes are better value for money for the route you mention, so I can certainly recommend it if your trip fits.
You can look up train timetables and costs for all of your legs at the Hyperdia travel planning website and learn how to use Hyperdia for Japan Rail Pass holders through our video blog.
Hope this helps!